Incommensurate-Commensurate Transition in Two-Dimensional Sine-Gordon System

Abstract

The two-dimensional classical sine-Gordon system which contains a misfit parameter μ in one direction is investigated at a particular temperature. This model at that temperature is transformed into a one-dimensional free spinless Fermi system. The commensurate phase is stable when μ is smaller than the critical value μ_c. The fluctuating incommensurate state is realized when μ>μ_c. The mean misfit near the critical value μ_c behaves as (μ−μ_c)^1⁄2.
The Fourier transform of the correlation function is also calculated. In the incommensurate phase it has a delta-function and a logarithmically divergent term in addition to a broad peak. Its behavior can be understood in terms of the fluctuating discommensurations.